Tail behavior and almost sure growth rate of supOU processes
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929511596032000 |
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| author | Grahovac, Danijel Kevei, Peter |
| author_facet | Grahovac, Danijel Kevei, Peter |
| contents | In this paper we consider sample path growth of superpositions of Ornstein--Uhlenbeck type processes (supOU). SupOU processes are stationary infinitely divisible processes defined as integrals with respect to a random measure. They allow marginal distributions and correlations to be modeled independently. Our results show that the almost sure behavior is primarily governed by the tail of the marginal distribution. In particular, we obtain a general integral test for the sample path growth that covers both heavy-tailed and light-tailed scenarios. We also investigate the tail behavior of the marginal distributions in connection with the characteristics of the underlying random measure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08584 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tail behavior and almost sure growth rate of supOU processes Grahovac, Danijel Kevei, Peter Probability 60G17, 60F15 In this paper we consider sample path growth of superpositions of Ornstein--Uhlenbeck type processes (supOU). SupOU processes are stationary infinitely divisible processes defined as integrals with respect to a random measure. They allow marginal distributions and correlations to be modeled independently. Our results show that the almost sure behavior is primarily governed by the tail of the marginal distribution. In particular, we obtain a general integral test for the sample path growth that covers both heavy-tailed and light-tailed scenarios. We also investigate the tail behavior of the marginal distributions in connection with the characteristics of the underlying random measure. |
| title | Tail behavior and almost sure growth rate of supOU processes |
| topic | Probability 60G17, 60F15 |
| url | https://arxiv.org/abs/2402.08584 |